# CLASS-6ADDITION OF ALGEBRAIC EXPRESSION OF UNLIKE TERM WITH SAME VARIABLE & DIFFERENT POWER

ADDITION OF UNLIKE TERM WITH SAME VARIABLE & DIFFERENT POWER -

When adding algebraic expressions with unlike terms that contain the same variables but with different exponents, you can't directly combine these terms because they represent different powers of the same variable. However, you can simplify the expression by grouping terms with the same variables and then expressing the result in its simplest form. Here's how to do it step by step:

1. Identify Like Variables:- Examine the expressions and identify terms with the same variables, even if the exponents are different.
2. Group Terms by Variables:- Organize the terms into groups based on their common variables. Each group may contain terms with the same variable but different exponents.
3. Combine Terms Within Each Group:- For each group of terms with the same variable(s), combine them by adding or subtracting the coefficients, keeping the variable(s) and their exponents unchanged.
4. Write the Result:- Express the final result as a sum of the combined groups.

Here's an example of adding algebraic expressions with unlike terms that have the same variable but different exponents:

Example.1) Adding Expressions with Different Exponents

Given the expressions:

• 3x²+ 2x - 5x³
• 2x⁵- 4x²+ 1

Ans.)

Identify like variables and group the terms:

• Group 1:-  3x² and -4x² (both contain the variable "x²").
• Group 2:-  2x and 0 (there is no "x" term in the second expression).
• Group 3:- -5x³, 2x⁵, and 1 (these terms contain different powers of "x").

Combine terms within each group:

• Group 1:-  3x²- 4x² = -x².
• Group 2:-  2x + 0 = 2x.
• Group 3:- -5x³+ 2x⁵ + 1 (no further simplification possible within this group).

Write the result as a sum of the combined groups:

• (-x²) + (2x) + (-5x³+ 2x⁵ + 1)

So, the simplified expression with unlike terms that have the same variable but different exponents is: 2x⁵ - 5x³- x²+ 2x + 1.

Example.2) Adding Expressions with Variables of Different Powers

Given the expressions:

• 3x²+ 2x - 5x³
• 4x - x²+ 7x³

Ans.)

Identify and group similar terms:

• Group 1:-  3x² and -x² (both involve the variable "x" with different exponents).
• Group 2:-  2x and 4x (both involve the variable "x" with different exponents).
• Group 3:- -5x³ and 7x³ (both involve the variable "x" with different exponents).

Now, combine the like terms within each group:

• Group 1:-  3x²- x²= 2x².
• Group 2:-  2x + 4x = 6x.
• Group 3:- -5x³+ 7x³= 2x³.

Write the result as a sum of the combined terms and any remaining terms:

• 2x²+ 6x + 2x³.

So, the simplified expression with unlike terms that contain the same variables with different powers is 2x²+ 6x + 2x³.

"Unlike terms" are terms that contain the same variables having different power.

7x²y⁵ and -2x³y⁵ These are NOT like terms since the exponents on x are different. These are unlike terms.

3.)  5a², 19b², c²

= 5a²+ 19b²+ c²

(All are unlike terms so we cannot add their coefficients)

4.) Add: 11a²+ 8b²- 9c², 5b²+ 3c²- 4a² and 3a²- 4b²- 4c².

Ans.)

Writing the terms of the given expressions in the same order in form of rows with like terms below each other and adding column wise;

11a²+ 8b²- 9c²

- 4a²+ 5b²+ 3c²

3a²- 4b²- 4c²

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10a²+ 9b²- 10c²

In this example, we combined the terms with the same variable "x" but different exponents, resulting in a simplified expression with like terms.